After you have changed the password with the command

 mysqladmin -u root password yourrootsqlpassword

you cannot set

mysqladmin -h server1.example.com -u root password yourrootsqlpassword

beaucose the password was changed and you have this

error: 'Host 'server1.example.com' is not allowed to connect to this mysql server'

now you have to supply the password set before, please correct the command in

mysqladmin -h server1.example.com -u root -p yourrootsqlpassword password yourrootsqlpassword

thank you.